Bisimulation for Impure Simplicial Complexes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910499833118720 |
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| author | Bílková, Marta van Ditmarsch, Hans Kuznets, Roman Randrianomentsoa, Rojo |
| author_facet | Bílková, Marta van Ditmarsch, Hans Kuznets, Roman Randrianomentsoa, Rojo |
| contents | As an alternative to Kripke models, simplicial complexes are a versatile semantic primitive on which to interpret epistemic logic. Given a set of vertices, a simplicial complex is a downward closed set of subsets, called simplexes, of the vertex set. A maximal simplex is called a facet. Impure simplicial complexes represent that some agents (processes) are dead. It is known that impure simplicial complexes categorically correspond to so-called partial epistemic (Kripke) models. In this contribution, we define a notion of bisimulation to compare impure simplicial complexes and show that it has the Hennessy-Milner property. These results are for a logical language including atoms that express whether agents are alive or dead. Without these atoms no reasonable standard notion of bisimulation exists, as we amply justify by counterexamples, because such a restricted language is insufficiently expressive. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_16785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bisimulation for Impure Simplicial Complexes Bílková, Marta van Ditmarsch, Hans Kuznets, Roman Randrianomentsoa, Rojo Logic in Computer Science Distributed, Parallel, and Cluster Computing As an alternative to Kripke models, simplicial complexes are a versatile semantic primitive on which to interpret epistemic logic. Given a set of vertices, a simplicial complex is a downward closed set of subsets, called simplexes, of the vertex set. A maximal simplex is called a facet. Impure simplicial complexes represent that some agents (processes) are dead. It is known that impure simplicial complexes categorically correspond to so-called partial epistemic (Kripke) models. In this contribution, we define a notion of bisimulation to compare impure simplicial complexes and show that it has the Hennessy-Milner property. These results are for a logical language including atoms that express whether agents are alive or dead. Without these atoms no reasonable standard notion of bisimulation exists, as we amply justify by counterexamples, because such a restricted language is insufficiently expressive. |
| title | Bisimulation for Impure Simplicial Complexes |
| topic | Logic in Computer Science Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2406.16785 |